A new calculation of the work of formation of bubbles and drops

Abstract

The thermodynamic basis of surface tension for bubbles and drops is reformulated to take into account the variation in surface tension for very small, growing or incipient bubbles and drops. After assessing the magnitudes involved by means of conventional theory, a model is put forward for this variation that avoids the supposition of extreme pressures at small sizes in the simple model. The parameter of this new model is then set by consideration of the properties of real gases, determined by analysis of the incipient bubble and then extended, it is argued, to the incipient drop. van der Waals' model of a real gas is used to show how this combines with the Lewins model in a self-consistent approach to the thermodynamics of surface tension for bubbles and drops. The changes from the simple theory will then allow a revision of the dynamic statistical theory of auto-nucleation and a reassessment of the critical sizes for imposed or heterogeneous nucleation, based on a simple and self-consistent thermodynamic model.

A reformulation of the fundamental thermodynamics of surface tension for spherical bubbles and drops

“…Of course we assume an equilibrium state to arrive at KelvinÕs formula, an assumption that is not fully justified and leads only to a bound of the real, dynamic process of the formation of a drop or bubble. Studies [11] have shown that the work of formation of the bubble at vanishing radius is small; it rises to a critical value at a corresponding critical size; and then decreases, becoming negative at larger size. And clearly as the radius goes to infinity, the plane case, we have instability since we have assumed that p e 6 ¼ p sat .…”